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Davis Guggenheim wanted to make his documentary to understand where Malala found her courage and drive

It's been three years since the name Malala Yousafzai entered the collective consciousness, when the then unknown 15-year-old Pakistani girl was shot by the Taliban for defying their ban on female education in the country's Swat Valley.

Her subsequent fight for survival and renewed vigour on recovery have proved an inspiration to millions around the world. Her courage has won her the Nobel Peace Prize and led to her becoming one of those rare individuals who can go by their first name alone.

But behind her international profile is one of a normal teenager - and a daughter of a loving, united and inspirational family.

It's this story, seemingly mundane yet so fundamental to who Malala is, that fascinated director Davis Guggenheim - maker of the Oscar-winning portrayal of US Democratic politician Al Gore in An Inconvenient Truth - and led to his latest documentary He Named Me Malala.

Guggenheim uses one-to-one interviews, news footage and animation to paint an intimate portrait of the Yousafzais's past and present - and in particular the influence of Malala's father Ziauddin on her life.

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The Yousafzai family worked with Davis Guggenheim over a period of 18 months

The director explains: "People in the Swat Valley were being killed for standing up to the Taliban but there was this young girl who decided she was going to stand up to them.

"People don't fully understand this vital element of her story or where that determination comes from.

"My first instinct in making this movie was that it is very much about a family, about a father's love and about a girl who feels empowered to do amazing things.

"If you cover that story, it speaks to girls all over the world."

Guggenheim filmed the Yousafzai family - Malala, her parents and two younger brothers - over 18 months.

Much of the film takes place at the family's home in Birmingham, where they stayed following Malala's treatment at the city's hospital.

But Guggenheim also shows Malala on trips to the Middle East and Africa as part of her work for the Malala Fund - an education charity she established with her father - visiting schools, refugee camps and addressing world leaders.

Guggenheim is himself passionate about the importance of education and has made documentaries on the US school system.

And as a father to two girls, he seems the perfect candidate to enter Malala's world - but it didn't prevent the nerves that preceded their first encounter.

"I was walking on eggshells," he says.

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In Pakistan, Ziauddin Yousafzai was a passionate social activist and a teacher, even establishing his own school, and was threatened by the Taliban

"But they were just hilarious and joyful. They tease each other and I found them remarkably enlightened and infinitely curious. I would leave their house invigorated.

"They have a certain freedom from having risked their lives and Malala lives her life even more fearlessly - the little things in life just disappear."

Malala's brothers Khushal, 15, and Atal, 11, are lively boys, dreaming of glorious futures and tirelessly jibing and arguing with their sister.

"Look Malala, one day I will be an astronaut and a great sportsman and you will be known as my sister," says Atal.

Her mother Toor Pekai is barely visible on camera due to her Pashtun sense of modesty but, says Guggenheim, she is "100% in control. When a big decision is being made all eyes turn to her".

And Malala emerges as a just a normal teenager, struggling to get the best grades at school and bashfully doe-eyed over Roger Federer.

It's an endearing picture but what truly stands out in this family story is Malala's bond with her father, who very visibly supports her in everything she wants to do.

It's an attachment that began even before Malala was born.

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Malala's father says he knew she would be special from the moment he first saw her

In Pakistan, Ziauddin belied his slight physique and the difficulties of a stammer to become a passionate social activist and a teacher, even establishing his own school.

In a patriarchal society in which "women are not known in public and their names are only known to family members", he was adamant his daughter would be different and named her after a legendary 19th Century Pashtun warrior heroine, Malalai of Maiwund.

"Malalai had had a voice and I wanted my Malala to have the same - that she would have freedom and be brave and be known by her name," says Ziauddin.

And it was immediately apparent she was special, he says.

"I hesitate to romanticise or make it something superstitious by saying she was born a saint or prophet but I felt an immediate attachment to her. I saw a light in her eyes.

"She was very mature and sensible and mindful of others and was loved by the whole community."

Ziauddin put himself at considerable risk through his activism and received threats from the Taliban as a result. It caused Malala extreme anxiety yet she continued with her own activism and famously wrote a blog for the BBC under a pseudonym, about life in the Swat Valley.

Though acknowledging he was a role model for his daughter, Ziauddin says he feels no guilt for what ultimately happened to her.

"Guilt comes from when you do something sinful. When your basic human rights are violated and you don't stand up, that's a sin," he says.

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Malala - here meeting Senate Minority Whip Richard Durbin - will be a leader and voice for young women for a long time to come, says Davis Guggenheim

"I didn't push my daughter; if I had she would have stopped. She would have said: 'Father you put me in a very bad situation, I got hit by a bullet, I am not going to do it anymore for you'.

"But she became more resilient, more committed and I've never heard her utter a single sigh or a single word which implies complaint or regret."

And Malala - who has been left with some paralysis in her face and impaired hearing - vehemently backs her father.

"My father only gave me the name Malalai. He didn't make me Malalai. I chose this life," she says.

As for the future, Ziauddin shows characteristic defiance. He is sure the family will go back to Pakistan for good, he says, despite the welcome and freedom they are all grateful to have received in the UK.

And he has faith that his daughter will know the right path for herself to tread. Guggenheim fully agrees.

"When you do the DNA of Malala, she is a potent mix of both her parents. She gets her sense of mission from her father but her moral fibre, her religious clarity and forgiveness from her mother," he says.

"Anything is possible for Malala. She is wholly equipped to be a leader and she is completely unique in that, when the big decisions are being made about girls education, she is the only young person at the table.

"She's a voice for all those girls who don't have a voice. She'll be that for a very long time."